[PDF] The Product Of Two Normally Distributed Random Variables eBook

Author : Norman L. Johnson
Publisher : John Wiley & Sons
Page : 747 pages
File Size : 39,8 MB
Release : 1995-05-08
Category : Mathematics
ISBN : 0471584940

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Comprehensive reference for statistical distributions Continuous Univariate Distributions, Volume 2 provides in-depth reference for anyone who applies statistical distributions in fields including engineering, business, economics, and the sciences. Covering a range of distributions, both common and uncommon, this book includes guidance toward extreme value, logistics, Laplace, beta, rectangular, noncentral distributions and more. Each distribution is presented individually for ease of reference, with clear explanations of methods of inference, tolerance limits, applications, characterizations, and other important aspects, including reference to other related distributions.

Author :
Publisher :
Page : 14 pages
File Size : 40,55 MB
Release : 1971
Category :
ISBN :

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Let W=UV where U and V are independent random variables. It is shown that if V is distributed according to the non-central Chi-square distribution, then W is distributed according to the Chi-square distribution if and only if U=1 with probability 1. If V is normally distributed, it is shown that W is normally distributed if and only if the distribution of U is a two-point distribution.

Author : Melvin Dale Springer
Publisher : John Wiley & Sons
Page : 510 pages
File Size : 28,12 MB
Release : 1979
Category : Mathematics
ISBN :

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Differentiation and integration in the complex plane; The distribution of sums and differences of Random variables; The distribution of products and quotients of Random variables; The distribution of algebraic functions of independent Random variables; The distribution of algebraic functions of independent H-function variables; Analytical model for evaluation of the H-function inversion integral; Approximating the distribution of an algebraic function of independent random variables; Distribution problems in statistics.

Author : Carl Edward Rasmussen
Publisher : MIT Press
Page : 266 pages
File Size : 32,58 MB
Release : 2005-11-23
Category : Computers
ISBN : 026218253X

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A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Author : David F. Anderson
Publisher : Cambridge University Press
Page : 447 pages
File Size : 50,55 MB
Release : 2017-11-02
Category : Mathematics
ISBN : 110824498X

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This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

Author : Mohammad Ahsanullah
Publisher : Springer Science & Business Media
Page : 163 pages
File Size : 34,43 MB
Release : 2014-02-07
Category : Mathematics
ISBN : 9462390614

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The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 21,20 MB
Release : 2018-09-27
Category : Business & Economics
ISBN : 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.